T-structures, T-functions, and texts (Q685376)

The paper introduces the notion of a text as a generalization of a word in the theory of formal languages. A text not only provides a word of letters but also gives a (grammatical) structure to this word. In this sense a text resembles a parse tree of a sentence. However, the structure given by a text need not be a tree, but can be a more general directed graph. Formally, a text \(\tau=(\lambda,\rho_ 1,\rho_ 2)\) consists of two linear orders \(\rho_ 1\) and \(\rho_ 2\) of the finite domain together with a labeling function \(\lambda\). The first linear order may be considered to form the word together with the labeling function, and the second linear order provides the structure of this word. The texts have their origin in the authors' 2-structures, and the formal treatment of texts makes use of the decomposition theorem of these graph- theoretical structures.